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Analytical Properties of Nonlinear Partial Differential Equations: with Applications to Shallow Water Models: 10 (CMS/CAIMS Books in Mathematics, 10) - Hardcover

Cheviakov, Alexei; Shanghai Maritime University

 
9783031530739: Analytical Properties of Nonlinear Partial Differential Equations: with Applications to Shallow Water Models: 10 (CMS/CAIMS Books in Mathematics, 10)
Hardcover
ISBN 10: 303153073X ISBN 13: 9783031530739
Publisher: Springer, 2024

Synopsis

Nonlinear partial differential equations (PDE) are at the core of mathematical modeling. In the past decades and recent years, multiple analytical methods to study various aspects of the mathematical structure of nonlinear PDEs have been developed. Those aspects include C- and S-integrability, Lagrangian and Hamiltonian formulations, equivalence transformations, local and nonlocal symmetries, conservation laws, and more. Modern computational approaches and symbolic software can be employed to systematically derive and use such properties, and where possible, construct exact and approximate solutions of nonlinear equations. This book contains a consistent overview of multiple properties of nonlinear PDEs, their relations, computation algorithms, and a uniformly presented set of examples of application of these methods to specific PDEs. Examples include both well known nonlinear PDEs and less famous systems that arise in the context of shallow water waves and far beyond. The book will beof interest to researchers and graduate students in applied mathematics, physics, and engineering, and can be used as a basis for research, study, reference, and applications.

"synopsis" may belong to another edition of this title.

From the Back Cover

Nonlinear partial differential equations (PDE) are at the core of mathematical modeling. In the past decades and recent years, multiple analytical methods to study various aspects of the mathematical structure of nonlinear PDEs have been developed. Those aspects include C- and S-integrability, Lagrangian and Hamiltonian formulations, equivalence transformations, local and nonlocal symmetries, conservation laws, and more. Modern computational approaches and symbolic software can be employed to systematically derive and use such properties, and where possible, construct exact and approximate solutions of nonlinear equations. This book contains a consistent overview of multiple properties of nonlinear PDEs, their relations, computation algorithms, and a uniformly presented set of examples of application of these methods to specific PDEs. Examples include both well known nonlinear PDEs and less famous systems that arise in the context of shallow water waves and far beyond. The book will be of interest to researchers and graduate students in applied mathematics, physics, and engineering, and can be used as a basis for research, study, reference, and applications.

"About this title" may belong to another edition of this title.

Publisher
Springer
Publication date
2024
Language
English
ISBN 10 
303153073X
ISBN 13 
9783031530739
Binding
Hardcover
Number of pages
327